Available bandwidth typically depends on the carrier frequency, and as an estimate it is around one-tenth of the carrier frequency (bps)

No. First, you are confusing the layman meaning of "bandwidth" (used to measure data rates) with the technical meaning (which is measured in Hertz). Second, there is no fixed relationship between center frequency and bandwidth. You can have a 1 Hz bandwidth @ 10 GHz or a 100 MHz bandwidth @ 50 MHz. Last, even when talking about bits/s, your data rate is dependent on the noise level and modulation scheme. 4096-QAM transmits 12 bits per Hz of bandwidth, but requires a highly noise-free environment. Alternatively, BPSK only transmits 1 bit per Hz but is highly noise-resistant.

In short, there are far too many factors to consider for any kind of relationship like you proposed to be useful.

As an aside, "carrier frequency" is no longer a useful concept for most modern modulation schemes. FM and AM radio have it, but it's a waste of power in most situations because it does not transmit any information by itself. It just makes construction of the receiver slightly easier (a useful thing in the very early days of radio). "Center frequency" is the equivalent modern concept.